Details

Time bar (total: 32.2s)

sample436.0ms

Algorithm
intervals
Results
129.0ms70×body2560valid
112.0ms132×body1280valid
109.0ms27×body5120valid
42.0ms83×body640valid
12.0ms35×body320valid
7.0ms59×body80valid
5.0ms21×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (666.0ms)

IterNodesCost
01925
14425
214525
372123
4390121
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
0.8b
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
18.4b
(/ (pow t 3.0) (* l l))
27.3b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
333×times-frac
291×add-exp-log
149×unpow-prod-down
137×div-exp
135×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
111×prod-exp
70×add-cbrt-cube
60×associate-*l/
57×associate-/r/
40×tan-quot
34×pow-exp
32×div-inv
25×cbrt-unprod
24×cbrt-undiv pow-to-exp
20×frac-times associate-*r/ associate-/l*
19×associate-/r*
13×sqr-pow
9×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* pow-prod-down clear-num
1×associate-*l* *-commutative associate-/l/
Counts
4 → 358
Calls
4 calls:
37.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
35.0ms
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
5.0ms
(/ (pow t 3.0) (* l l))
55.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
321.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
447.0ms
(/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)))
177.0ms
(/ (pow t 3.0) (* l l))
553.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify652.0ms

Counts
370 → 370
Iterations

Useful iterations: done (637.0ms)

IterNodesCost
065510619
1160110097
done500010064

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.6b
(* (pow k 2.0) (pow t 1.0))
15.9b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
1597×add-exp-log
1095×prod-exp
882×pow-exp
668×div-exp
492×pow-to-exp
130×rec-exp 1-exp
37×add-sqr-sqrt
32×unpow-prod-down
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
19×times-frac associate-*r*
18×associate-*l*
14×sqr-pow
12×unswap-sqr
8×associate-/r*
6×cbrt-unprod
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u unpow2 add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 575
Calls
4 calls:
1.0ms
(pow (sin k) 2)
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms
(* (pow k 2.0) (pow t 1.0))
38.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
331.0ms
(* (pow k 2.0) (pow t 1.0))
678.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Counts
587 → 587
Iterations

Useful iterations: 2 (639.0ms)

IterNodesCost
044614510
1114012421
2294812185
done500112185

prune612.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b
(pow (sin k) 2)
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.9b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1468
Calls
4 calls:
22.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.0ms
(pow (sin k) 2)
7.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
66.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
344.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
19.0ms
(pow (sin k) 2)
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
638.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.2s

Counts
1480 → 1480
Iterations

Useful iterations: 2 (662.0ms)

IterNodesCost
060550477
1170031964
2359331674
done500131674

prune604.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.8b
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.9b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite975.0ms

Algorithm
rewrite-expression-head
Rules
22078×add-exp-log
15966×prod-exp
12575×pow-exp
9172×div-exp
6095×pow-to-exp
1310×rec-exp 1-exp
37×add-cbrt-cube
31×unpow-prod-down
29×times-frac
26×associate-*l*
25×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r*
8×cbrt-undiv
7×sqr-pow
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 4466
Calls
4 calls:
8.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
120.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
39.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
342.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
655.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
648.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.7s

Counts
4478 → 4478
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01213193011
13558150255
done5001150187

prune767.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.7b

regimes370.0ms

Accuracy

34.7% (4.3b remaining)

Error of 16.2b against oracle of 11.8b and baseline of 18.5b

bsearch700.0ms

Steps
ItersRangePoint
9
2.795908276359606e+144
8.311157809269943e+150
8.17383998183876e+150
7
-7.368854766727216e+156
-6.720595982684725e+154
-6.863479513964647e+154

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
047110
16081
done6081

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.1s2164×body2560valid
3.9s913×body5120valid
3.4s4089×body1280valid
1.3s2490×body640valid
363.0ms1005×body320valid
253.0ms2023×body80valid
106.0ms444×body160valid